फलन ` f(x) = sin^(-1) ( 2x sqrt( 1- x^(2) ) ) " का " sin^(-1) ` के सापेक्ष अवकल गुणांक ज्ञात करे ।

Explanation

माना `y _(1) = sin ^(-1) 2x sqrt( 1- x^(2))`
`x = sin theta ` रखने पर ,
`y-(1) = sin ^(-1) ( 2 sin theta sqrt( 1- sin^(2) theta )=sin ^(-1) ( 2 sin theta cos theta )`
` y_(1) = sin^(1) ( sin 2 theta) `
` y_(1) = 2 theta = 2 sin ^(-1) x `
` (dy_(1))/(dx) = 2/ sqrt(1-x^(2))`
पुनः `y_(2) = sin^(-1) x `
` (dy_(2))/(dx) = 1/(sqrt(1-x^(2)))`
तब ` (dsin^(-1) (2x sqrt( 1- x^(2))))/(d sin ^(-1) x ) = (2/sqrt(1-x^(2)))/ (1/(sqrt(1-x^(2))))`